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Title: Representation and Measure of Structural Information
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Abstract: We introduce a uniform representation of general objects that captures the regularities with respect to their structure. It allows a representation of a general class of objects including geometric patterns and images in a sparse, modular, hierarchical, and recursive manner. The representation can exploit any computable regularity in objects to compactly describe them, while also being capable of representing random objects as raw data. A set of rules uniformly dictates the interpretation of the representation into raw signal, which makes it possible to ask what pattern a given raw signal contains. Also, it allows simple separation of the information that we wish to ignore from that which we measure, by using a set of maps to delineate the a priori parts of the objects, leaving only the information in the structure. Using the representation, we introduce a measure of information in general objects relative to structures defined by the set of maps. We point out that the common prescription of encoding objects by strings to use Kolmogorov complexity is meaningless when, as often is the case, the encoding is not specified in any way other than that it exists. Noting this, we define the measure directly in terms of the structures of the spaces in which the objects reside. As a result, the measure is defined relative to a set of maps that characterize the structures. It turns out that the measure is equivalent to Kolmogorov complexity when it is defined relative to the maps characterizing the structure of natural numbers. Thus, the formulation gives the larger class of objects a meaningful measure of information that generalizes Kolmogorov complexity.
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Title: Adaptive optimal allocation in stratified sampling methods
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Abstract: In this paper, we propose a stratified sampling algorithm in which the random drawings made in the strata to compute the expectation of interest are also used to adaptively modify the proportion of further drawings in each stratum. These proportions converge to the optimal allocation in terms of variance reduction. And our stratified estimator is asymptotically normal with asymptotic variance equal to the minimal one. Numerical experiments confirm the efficiency of our algorithm.
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Title: Signed Chord Length Distribution. I
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Abstract: In this paper is discussed an application of signed measures (charges) to description of segment and chord length distributions in nonconvex bodies. The signed distribution may naturally appears due to definition via derivatives of nonnegative autocorrelation function simply related with distances distribution between pairs of points in the body. In the work is suggested constructive geometrical interpretation of such derivatives and illustrated appearance of "positive" and "negative" elements similar with usual Hanh-Jordan decomposition in measure theory. The construction is also close related with applications of Dirac method of chords.
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Title: Circumspect descent prevails in solving random constraint satisfaction problems
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Abstract: We study the performance of stochastic local search algorithms for random instances of the $K$-satisfiability ($K$-SAT) problem. We introduce a new stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by \em never going upwards in energy. ChainSAT is a algorithm in the sense that it considers only variables occurring in unsatisfied clauses. We show by extensive numerical investigations that ChainSAT and other focused algorithms solve large $K$-SAT instances almost surely in linear time, up to high clause-to-variable ratios $\alpha$; for example, for K=4 we observe linear-time performance well beyond the recently postulated clustering and condensation transitions in the solution space. The performance of ChainSAT is a surprise given that by design the algorithm gets trapped into the first local energy minimum it encounters, yet no such minima are encountered. We also study the geometry of the solution space as accessed by stochastic local search algorithms.
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Title: A Method for Compressing Parameters in Bayesian Models with Application to Logistic Sequence Prediction Models
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Abstract: Bayesian classification and regression with high order interactions is largely infeasible because Markov chain Monte Carlo (MCMC) would need to be applied with a great many parameters, whose number increases rapidly with the order. In this paper we show how to make it feasible by effectively reducing the number of parameters, exploiting the fact that many interactions have the same values for all training cases. Our method uses a single ``compressed'' parameter to represent the sum of all parameters associated with a set of patterns that have the same value for all training cases. Using symmetric stable distributions as the priors of the original parameters, we can easily find the priors of these compressed parameters. We therefore need to deal only with a much smaller number of compressed parameters when training the model with MCMC. The number of compressed parameters may have converged before considering the highest possible order. After training the model, we can split these compressed parameters into the original ones as needed to make predictions for test cases. We show in detail how to compress parameters for logistic sequence prediction models. Experiments on both simulated and real data demonstrate that a huge number of parameters can indeed be reduced by our compression method.
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Title: Auxiliary Information and A Priori Values in Construction of Improved Estimators
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Abstract: This volume is a collection of six papers on the use of auxiliary information and 'a priori' values in construction of improved estimators. The work included here will be of immense application for researchers and students who emply auxiliary information in any form.
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Title: On the Relationship between the Posterior and Optimal Similarity
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Abstract: For a classification problem described by the joint density $P(\omega,x)$, models of $P(\omega\eq\omega'|x,x')$ (the ``Bayesian similarity measure'') have been shown to be an optimal similarity measure for nearest neighbor classification. This paper analyzes demonstrates several additional properties of that conditional distribution. The paper first shows that we can reconstruct, up to class labels, the class posterior distribution $P(\omega|x)$ given $P(\omega\eq\omega'|x,x')$, gives a procedure for recovering the class labels, and gives an asymptotically Bayes-optimal classification procedure. It also shows, given such an optimal similarity measure, how to construct a classifier that outperforms the nearest neighbor classifier and achieves Bayes-optimal classification rates. The paper then analyzes Bayesian similarity in a framework where a classifier faces a number of related classification tasks (multitask learning) and illustrates that reconstruction of the class posterior distribution is not possible in general. Finally, the paper identifies a distinct class of classification problems using $P(\omega\eq\omega'|x,x')$ and shows that using $P(\omega\eq\omega'|x,x')$ to solve those problems is the Bayes optimal solution.
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Title: Learning Similarity for Character Recognition and 3D Object Recognition
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Abstract: I describe an approach to similarity motivated by Bayesian methods. This yields a similarity function that is learnable using a standard Bayesian methods. The relationship of the approach to variable kernel and variable metric methods is discussed. The approach is related to variable kernel Experimental results on character recognition and 3D object recognition are presented..
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Title: Learning View Generalization Functions
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Abstract: Learning object models from views in 3D visual object recognition is usually formulated either as a function approximation problem of a function describing the view-manifold of an object, or as that of learning a class-conditional density. This paper describes an alternative framework for learning in visual object recognition, that of learning the view-generalization function. Using the view-generalization function, an observer can perform Bayes-optimal 3D object recognition given one or more 2D training views directly, without the need for a separate model acquisition step. The paper shows that view generalization functions can be computationally practical by restating two widely-used methods, the eigenspace and linear combination of views approaches, in a view generalization framework. The paper relates the approach to recent methods for object recognition based on non-uniform blurring. The paper presents results both on simulated 3D ``paperclip'' objects and real-world images from the COIL-100 database showing that useful view-generalization functions can be realistically be learned from a comparatively small number of training examples.
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Title: View Based Methods can achieve Bayes-Optimal 3D Recognition
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Abstract: This paper proves that visual object recognition systems using only 2D Euclidean similarity measurements to compare object views against previously seen views can achieve the same recognition performance as observers having access to all coordinate information and able of using arbitrary 3D models internally. Furthermore, it demonstrates that such systems do not require more training views than Bayes-optimal 3D model-based systems. For building computer vision systems, these results imply that using view-based or appearance-based techniques with carefully constructed combination of evidence mechanisms may not be at a disadvantage relative to 3D model-based systems. For computational approaches to human vision, they show that it is impossible to distinguish view-based and 3D model-based techniques for 3D object recognition solely by comparing the performance achievable by human and 3D model-based systems.
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Title: A Spectral Approach to Analyzing Belief Propagation for 3-Coloring
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Abstract: Contributing to the rigorous understanding of BP, in this paper we relate the convergence of BP to spectral properties of the graph. This encompasses a result for random graphs with a ``planted'' solution; thus, we obtain the first rigorous result on BP for graph coloring in the case of a complex graphical structure (as opposed to trees). In particular, the analysis shows how Belief Propagation breaks the symmetry between the $3!$ possible permutations of the color classes.
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Title: Summarization and Classification of Non-Poisson Point Processes
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Abstract: Fitting models for non-Poisson point processes is complicated by the lack of tractable models for much of the data. By using large samples of independent and identically distributed realizations and statistical learning, it is possible to identify absence of fit through finding a classification rule that can efficiently identify single realizations of each type. The method requires a much wider range of descriptive statistics than are currently in use, and a new concept of model fitting which is derive from how physical laws are judged to fit data.
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Title: Pac-Bayesian Supervised Classification: The Thermodynamics of Statistical Learning
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Abstract: This monograph deals with adaptive supervised classification, using tools borrowed from statistical mechanics and information theory, stemming from the PACBayesian approach pioneered by David McAllester and applied to a conception of statistical learning theory forged by Vladimir Vapnik. Using convex analysis on the set of posterior probability measures, we show how to get local measures of the complexity of the classification model involving the relative entropy of posterior distributions with respect to Gibbs posterior measures. We then discuss relative bounds, comparing the generalization error of two classification rules, showing how the margin assumption of Mammen and Tsybakov can be replaced with some empirical measure of the covariance structure of the classification model.We show how to associate to any posterior distribution an effective temperature relating it to the Gibbs prior distribution with the same level of expected error rate, and how to estimate this effective temperature from data, resulting in an estimator whose expected error rate converges according to the best possible power of the sample size adaptively under any margin and parametric complexity assumptions. We describe and study an alternative selection scheme based on relative bounds between estimators, and present a two step localization technique which can handle the selection of a parametric model from a family of those. We show how to extend systematically all the results obtained in the inductive setting to transductive learning, and use this to improve Vapnik's generalization bounds, extending them to the case when the sample is made of independent non-identically distributed pairs of patterns and labels. Finally we review briefly the construction of Support Vector Machines and show how to derive generalization bounds for them, measuring the complexity either through the number of support vectors or through the value of the transductive or inductive margin.
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Title: Wavelet methods in statistics: Some recent developments and their applications
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Abstract: The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in wavelet applications to statistics and to the analysis of experimental data, with many successes in the efficient analysis, processing, and compression of noisy signals and images. This is a selective review article that attempts to synthesize some recent work on ``nonlinear'' wavelet methods in nonparametric curve estimation and their role on a variety of applications. After a short introduction to wavelet theory, we discuss in detail several wavelet shrinkage and wavelet thresholding estimators, scattered in the literature and developed, under more or less standard settings, for density estimation from i.i.d. observations or to denoise data modeled as observations of a signal with additive noise. Most of these methods are fitted into the general concept of regularization with appropriately chosen penalty functions. A narrow range of applications in major areas of statistics is also discussed such as partial linear regression models and functional index models. The usefulness of all these methods are illustrated by means of simulations and practical examples.
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Title: A Reactive Tabu Search Algorithm for Stimuli Generation in Psycholinguistics
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Abstract: The generation of meaningless "words" matching certain statistical and/or linguistic criteria is frequently needed for experimental purposes in Psycholinguistics. Such stimuli receive the name of pseudowords or nonwords in the Cognitive Neuroscience literatue. The process for building nonwords sometimes has to be based on linguistic units such as syllables or morphemes, resulting in a numerical explosion of combinations when the size of the nonwords is increased. In this paper, a reactive tabu search scheme is proposed to generate nonwords of variables size. The approach builds pseudowords by using a modified Metaheuristic algorithm based on a local search procedure enhanced by a feedback-based scheme. Experimental results show that the new algorithm is a practical and effective tool for nonword generation.
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Title: Equations of States in Singular Statistical Estimation
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Abstract: Learning machines which have hierarchical structures or hidden variables are singular statistical models because they are nonidentifiable and their Fisher information matrices are singular. In singular statistical models, neither the Bayes a posteriori distribution converges to the normal distribution nor the maximum likelihood estimator satisfies asymptotic normality. This is the main reason why it has been difficult to predict their generalization performances from trained states. In this paper, we study four errors, (1) Bayes generalization error, (2) Bayes training error, (3) Gibbs generalization error, and (4) Gibbs training error, and prove that there are mathematical relations among these errors. The formulas proved in this paper are equations of states in statistical estimation because they hold for any true distribution, any parametric model, and any a priori distribution. Also we show that Bayes and Gibbs generalization errors are estimated by Bayes and Gibbs training errors, and propose widely applicable information criteria which can be applied to both regular and singular statistical models.
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Title: Computational Chemotaxis in Ants and Bacteria over Dynamic Environments
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Abstract: Chemotaxis can be defined as an innate behavioural response by an organism to a directional stimulus, in which bacteria, and other single-cell or multicellular organisms direct their movements according to certain chemicals in their environment. This is important for bacteria to find food (e.g., glucose) by swimming towards the highest concentration of food molecules, or to flee from poisons. Based on self-organized computational approaches and similar stigmergic concepts we derive a novel swarm intelligent algorithm. What strikes from these observations is that both eusocial insects as ant colonies and bacteria have similar natural mechanisms based on stigmergy in order to emerge coherent and sophisticated patterns of global collective behaviour. Keeping in mind the above characteristics we will present a simple model to tackle the collective adaptation of a social swarm based on real ant colony behaviors (SSA algorithm) for tracking extrema in dynamic environments and highly multimodal complex functions described in the well-know De Jong test suite. Later, for the purpose of comparison, a recent model of artificial bacterial foraging (BFOA algorithm) based on similar stigmergic features is described and analyzed. Final results indicate that the SSA collective intelligence is able to cope and quickly adapt to unforeseen situations even when over the same cooperative foraging period, the community is requested to deal with two different and contradictory purposes, while outperforming BFOA in adaptive speed. Results indicate that the present approach deals well in severe Dynamic Optimization problems.
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Title: Evolving localizations in reaction-diffusion cellular automata
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Abstract: We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in each one state. We employ evolutionary algorithms to breed local transition functions that support mobile localizations (gliders), and characterize sets of the functions selected in terms of quasi-chemical systems. Analysis of the set of functions evolved allows to speculate that mobile localizations are likely to emerge in the quasi-chemical systems with limited diffusion of one reagent, a small number of molecules is required for amplification of travelling localizations, and reactions leading to stationary localizations involve relatively equal amount of quasi-chemical species. Techniques developed can be applied in cascading signals in nature-inspired spatially extended computing devices, and phenomenological studies and classification of non-linear discrete systems.
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Title: A Universal Kernel for Learning Regular Languages
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Abstract: We give a universal kernel that renders all the regular languages linearly separable. We are not able to compute this kernel efficiently and conjecture that it is intractable, but we do have an efficient $\eps$-approximation.
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Title: Dimensionality Reduction and Reconstruction using Mirroring Neural Networks and Object Recognition based on Reduced Dimension Characteristic Vector
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Abstract: In this paper, we present a Mirroring Neural Network architecture to perform non-linear dimensionality reduction and Object Recognition using a reduced lowdimensional characteristic vector. In addition to dimensionality reduction, the network also reconstructs (mirrors) the original high-dimensional input vector from the reduced low-dimensional data. The Mirroring Neural Network architecture has more number of processing elements (adalines) in the outer layers and the least number of elements in the central layer to form a converging-diverging shape in its configuration. Since this network is able to reconstruct the original image from the output of the innermost layer (which contains all the information about the input pattern), these outputs can be used as object signature to classify patterns. The network is trained to minimize the discrepancy between actual output and the input by back propagating the mean squared error from the output layer to the input layer. After successfully training the network, it can reduce the dimension of input vectors and mirror the patterns fed to it. The Mirroring Neural Network architecture gave very good results on various test patterns.
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Title: Automatic Pattern Classification by Unsupervised Learning Using Dimensionality Reduction of Data with Mirroring Neural Networks
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Abstract: This paper proposes an unsupervised learning technique by using Multi-layer Mirroring Neural Network and Forgy's clustering algorithm. Multi-layer Mirroring Neural Network is a neural network that can be trained with generalized data inputs (different categories of image patterns) to perform non-linear dimensionality reduction and the resultant low-dimensional code is used for unsupervised pattern classification using Forgy's algorithm. By adapting the non-linear activation function (modified sigmoidal function) and initializing the weights and bias terms to small random values, mirroring of the input pattern is initiated. In training, the weights and bias terms are changed in such a way that the input presented is reproduced at the output by back propagating the error. The mirroring neural network is capable of reducing the input vector to a great degree (approximately 1/30th the original size) and also able to reconstruct the input pattern at the output layer from this reduced code units. The feature set (output of central hidden layer) extracted from this network is fed to Forgy's algorithm, which classify input data patterns into distinguishable classes. In the implementation of Forgy's algorithm, initial seed points are selected in such a way that they are distant enough to be perfectly grouped into different categories. Thus a new method of unsupervised learning is formulated and demonstrated in this paper. This method gave impressive results when applied to classification of different image patterns.
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Title: A Common View on Strong, Uniform, and Other Notions of Equivalence in Answer-Set Programming
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Abstract: Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are different concepts. The former holds, given programs P and Q, iff P can be faithfully replaced by Q within any context R, while the latter holds iff P and Q provide the same output, that is, they have the same answer sets. Notions in between strong and ordinary equivalence have been introduced as theoretical tools to compare incomplete programs and are defined by either restricting the syntactic structure of the considered context programs R or by bounding the set A of atoms allowed to occur in R (relativized equivalence).For the latter approach, different A yield properly different equivalence notions, in general. For the former approach, however, it turned out that any ``reasonable'' syntactic restriction to R coincides with either ordinary, strong, or uniform equivalence. In this paper, we propose a parameterization for equivalence notions which takes care of both such kinds of restrictions simultaneously by bounding, on the one hand, the atoms which are allowed to occur in the rule heads of the context and, on the other hand, the atoms which are allowed to occur in the rule bodies of the context. We introduce a general semantical characterization which includes known ones as SE-models (for strong equivalence) or UE-models (for uniform equivalence) as special cases. Moreover,we provide complexity bounds for the problem in question and sketch a possible implementation method. To appear in Theory and Practice of Logic Programming (TPLP).
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Title: Kernels and Ensembles: Perspectives on Statistical Learning
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Abstract: Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and ensemble methods. In this expository article, I discuss the main ideas behind these two types of methods, namely how to transform linear algorithms into nonlinear ones by using kernel functions, and how to make predictions with an ensemble or a collection of models rather than a single model. I also share my personal perspectives on how these ideas have influenced and shaped my own research. In particular, I present two recent algorithms that I have invented with my collaborators: LAGO, a fast kernel algorithm for unbalanced classification and rare target detection; and Darwinian evolution in parallel universes, an ensemble method for variable selection.
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Title: On Using Unsatisfiability for Solving Maximum Satisfiability
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Abstract: Maximum Satisfiability (MaxSAT) is a well-known optimization pro- blem, with several practical applications. The most widely known MAXS AT algorithms are ineffective at solving hard problems instances from practical application domains. Recent work proposed using efficient Boolean Satisfiability (SAT) solvers for solving the MaxSAT problem, based on identifying and eliminating unsatisfiable subformulas. However, these algorithms do not scale in practice. This paper analyzes existing MaxSAT algorithms based on unsatisfiable subformula identification. Moreover, the paper proposes a number of key optimizations to these MaxSAT algorithms and a new alternative algorithm. The proposed optimizations and the new algorithm provide significant performance improvements on MaxSAT instances from practical applications. Moreover, the efficiency of the new generation of unsatisfiability-based MaxSAT solvers becomes effectively indexed to the ability of modern SAT solvers to proving unsatisfiability and identifying unsatisfiable subformulas.
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Title: Cumulative and Averaging Fission of Beliefs
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Abstract: Belief fusion is the principle of combining separate beliefs or bodies of evidence originating from different sources. Depending on the situation to be modelled, different belief fusion methods can be applied. Cumulative and averaging belief fusion is defined for fusing opinions in subjective logic, and for fusing belief functions in general. The principle of fission is the opposite of fusion, namely to eliminate the contribution of a specific belief from an already fused belief, with the purpose of deriving the remaining belief. This paper describes fission of cumulative belief as well as fission of averaging belief in subjective logic. These operators can for example be applied to belief revision in Bayesian belief networks, where the belief contribution of a given evidence source can be determined as a function of a given fused belief and its other contributing beliefs.
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Title: Locality and low-dimensions in the prediction of natural experience from fMRI
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Abstract: Functional Magnetic Resonance Imaging (fMRI) provides dynamical access into the complex functioning of the human brain, detailing the hemodynamic activity of thousands of voxels during hundreds of sequential time points. One approach towards illuminating the connection between fMRI and cognitive function is through decoding; how do the time series of voxel activities combine to provide information about internal and external experience? Here we seek models of fMRI decoding which are balanced between the simplicity of their interpretation and the effectiveness of their prediction. We use signals from a subject immersed in virtual reality to compare global and local methods of prediction applying both linear and nonlinear techniques of dimensionality reduction. We find that the prediction of complex stimuli is remarkably low-dimensional, saturating with less than 100 features. In particular, we build effective models based on the decorrelated components of cognitive activity in the classically-defined Brodmann areas. For some of the stimuli, the top predictive areas were surprisingly transparent, including Wernicke's area for verbal instructions, visual cortex for facial and body features, and visual-temporal regions for velocity. Direct sensory experience resulted in the most robust predictions, with the highest correlation ($c \sim 0.8$) between the predicted and experienced time series of verbal instructions. Techniques based on non-linear dimensionality reduction (Laplacian eigenmaps) performed similarly. The interpretability and relative simplicity of our approach provides a conceptual basis upon which to build more sophisticated techniques for fMRI decoding and offers a window into cognitive function during dynamic, natural experience.
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Title: About Algorithm for Transformation of Logic Functions (ATLF)
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Abstract: In this article the algorithm for transformation of logic functions which are given by truth tables is considered. The suggested algorithm allows the transformation of many-valued logic functions with the required number of variables and can be looked in this sense as universal.
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Title: Stochastic adaptation of importance sampler
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Abstract: Improving efficiency of importance sampler is at the center of research in Monte Carlo methods. While adaptive approach is usually difficult within the Markov Chain Monte Carlo framework, the counterpart in importance sampling can be justified and validated easily. We propose an iterative adaptation method for learning the proposal distribution of an importance sampler based on stochastic approximation. The stochastic approximation method can recruit general iterative optimization techniques like the minorization-maximization algorithm. The effectiveness of the approach in optimizing the Kullback divergence between the proposal distribution and the target is demonstrated using several simple examples.
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Title: Sequential operators in computability logic
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Abstract: Computability logic (CL) (see http://www.cis.upenn.edu/ giorgi/cl.html) is a semantical platform and research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been. Formulas in CL stand for (interactive) computational problems, understood as games between a machine and its environment; logical operators represent operations on such entities; and "truth" is understood as existence of an effective solution, i.e., of an algorithmic winning strategy. The formalism of CL is open-ended, and may undergo series of extensions as the study of the subject advances. The main groups of operators on which CL has been focused so far are the parallel, choice, branching, and blind operators. The present paper introduces a new important group of operators, called sequential. The latter come in the form of sequential conjunction and disjunction, sequential quantifiers, and sequential recurrences. As the name may suggest, the algorithmic intuitions associated with this group are those of sequential computations, as opposed to the intuitions of parallel computations associated with the parallel group of operations: playing a sequential combination of games means playing its components in a sequential fashion, one after one. The main technical result of the present paper is a sound and complete axiomatization of the propositional fragment of computability logic whose vocabulary, together with negation, includes all three -- parallel, choice and sequential -- sorts of conjunction and disjunction. An extension of this result to the first-order level is also outlined.
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Title: Population stratification using a statistical model on hypergraphs
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Abstract: Population stratification is a problem encountered in several areas of biology and public health. We tackle this problem by mapping a population and its elements attributes into a hypergraph, a natural extension of the concept of graph or network to encode associations among any number of elements. On this hypergraph, we construct a statistical model reflecting our intuition about how the elements attributes can emerge from a postulated population structure. Finally, we introduce the concept of stratification representativeness as a mean to identify the simplest stratification already containing most of the information about the population structure. We demonstrate the power of this framework stratifying an animal and a human population based on phenotypic and genotypic properties, respectively.
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Title: Reconstruction of Markov Random Fields from Samples: Some Easy Observations and Algorithms
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Abstract: Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random fields. We analyze a simple algorithm for reconstructing the underlying graph defining a Markov random field on $n$ nodes and maximum degree $d$ given observations. We show that under mild non-degeneracy conditions it reconstructs the generating graph with high probability using $\Theta(d \epsilon^-2\delta^-4 \log n)$ samples where $\epsilon,\delta$ depend on the local interactions. For most local interaction $\eps,\delta$ are of order $\exp(-O(d))$. Our results are optimal as a function of $n$ up to a multiplicative constant depending on $d$ and the strength of the local interactions. Our results seem to be the first results for general models that guarantee that \em the generating model is reconstructed. Furthermore, we provide explicit $O(n^d+2 \epsilon^-2\delta^-4 \log n)$ running time bound. In cases where the measure on the graph has correlation decay, the running time is $O(n^2 \log n)$ for all fixed $d$. We also discuss the effect of observing noisy samples and show that as long as the noise level is low, our algorithm is effective. On the other hand, we construct an example where large noise implies non-identifiability even for generic noise and interactions. Finally, we briefly show that in some simple cases, models with hidden nodes can also be recovered.
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Title: Ontology and Formal Semantics - Integration Overdue
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Abstract: In this note we suggest that difficulties encountered in natural language semantics are, for the most part, due to the use of mere symbol manipulation systems that are devoid of any content. In such systems, where there is hardly any link with our common-sense view of the world, and it is quite difficult to envision how one can formally account for the considerable amount of content that is often implicit, but almost never explicitly stated in our everyday discourse. The solution, in our opinion, is a compositional semantics grounded in an ontology that reflects our commonsense view of the world and the way we talk about it in ordinary language. In the compositional logic we envision there are ontological (or first-intension) concepts, and logical (or second-intension) concepts, and where the ontological concepts include not only Davidsonian events, but other abstract objects as well (e.g., states, processes, properties, activities, attributes, etc.) It will be demonstrated here that in such a framework, a number of challenges in the semantics of natural language (e.g., metonymy, intensionality, metaphor, etc.) can be properly and uniformly addressed.
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Title: Efficient blind search: Optimal power of detection under computational cost constraints
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Abstract: Some astronomy projects require a blind search through a vast number of hypotheses to detect objects of interest. The number of hypotheses to test can be in the billions. A naive blind search over every single hypothesis would be far too costly computationally. We propose a hierarchical scheme for blind search, using various "resolution" levels. At lower resolution levels, "regions" of interest in the search space are singled out with a low computational cost. These regions are refined at intermediate resolution levels and only the most promising candidates are finally tested at the original fine resolution. The optimal search strategy is found by dynamic programming. We demonstrate the procedure for pulsar search from satellite gamma-ray observations and show that the power of the naive blind search can almost be matched with the hierarchical scheme while reducing the computational burden by more than three orders of magnitude.
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